Has anyone else come across this?
The starter ring fell off my flywheel (well clutch carrier to buy into BMW "Newspeak" a couple of years back - symptoms were near identical to what you describe.
It turns out that this is a sufficiently frequent occurance that sellers of 2nd had partsa think that their offerings are made of solid gold.
It is also the case that BMW had a couple of goes at using different size/composition rivets and that only the most recent ones appear to be immune.
On the basis of the prices demanded by wreckers and not wanting to have to deal with the matter again, I bought a new one.
Don't forget to mark your clutch pack so that it goes back with the same relative positions.
Also not a bad idea to replace oil pump deal and rear main seal whilst you are there, along with the gearbox input shaft seal.
Getting the gearbox off and the flywheel out is not a job you want to do too often.